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1. CJM 2013 (vol 66 pp. 141)
Existence of Taut Foliations on Seifert Fibered Homology $3$-spheres This paper concerns the problem of existence of taut foliations among $3$-manifolds.
Since the contribution of David Gabai,
we know that closed $3$-manifolds with non-trivial second homology group
admit a taut foliation.
The essential part of this paper focuses on Seifert fibered homology $3$-spheres.
The result is quite different if they are integral or rational but non-integral homology $3$-spheres.
Concerning integral homology $3$-spheres, we can see that all but the $3$-sphere and the PoincarÃ© $3$-sphere admit a taut foliation.
Concerning non-integral homology $3$-spheres,
we prove there are infinitely many which admit a taut foliation, and infinitely many without taut foliation.
Moreover, we show that the geometries do not determine the existence of taut foliations
on non-integral Seifert fibered homology $3$-spheres.
Keywords:homology 3-spheres, taut foliation, Seifert-fibered 3-manifolds Categories:57M25, 57M50, 57N10, 57M15 |
2. CJM 2008 (vol 60 pp. 164)
Boundary Structure of Hyperbolic $3$-Manifolds Admitting Annular and Toroidal Fillings at Large Distance |
Boundary Structure of Hyperbolic $3$-Manifolds Admitting Annular and Toroidal Fillings at Large Distance For a hyperbolic $3$-manifold $M$ with a torus boundary component,
all but finitely many Dehn fillings yield hyperbolic $3$-manifolds.
In this paper, we will focus on the situation where
$M$ has two exceptional Dehn fillings: an annular filling and a toroidal filling.
For such a situation, Gordon gave an upper bound of $5$ for the distance between such slopes.
Furthermore, the distance $4$ is realized only by two specific manifolds, and $5$
is realized by a single manifold.
These manifolds all have a union of two tori as their boundaries.
Also, there is a manifold with three tori as its boundary which realizes the distance $3$.
We show that if the distance is $3$ then the boundary of the manifold consists of at most three tori.
Keywords:Dehn filling, annular filling, toroidal filling, knot Categories:57M50, 57N10 |
3. CJM 2004 (vol 56 pp. 1022)
Non-Orientable Surfaces and Dehn Surgeries Let $K$ be a knot in $S^3$. This paper is devoted to Dehn surgeries which create
$3$-manifolds containing a closed non-orientable surface $\ch S$. We look at the
slope ${p}/{q}$ of the surgery, the Euler characteristic $\chi(\ch S)$ of the
surface and the intersection number $s$ between $\ch S$ and the core of the Dehn
surgery. We prove that if $\chi(\hat S) \geq 15 - 3q$, then $s=1$. Furthermore,
if $s=1$ then $q\leq 4-3\chi(\ch S)$ or $K$ is cabled and $q\leq 8-5\chi(\ch S)$.
As consequence, if $K$ is hyperbolic and $\chi(\ch S)=-1$, then $q\leq 7$.
Keywords:Non-orientable surface, Dehn surgery, Intersection graphs Categories:57M25, 57N10, 57M15 |